History matching of time-lapse crosswell data using ensemble kalman filtering

ABSTRACT

Data from crosswell seismic surveys is processed to provide crosswell time-lapse data to map fluid changes in a reservoir where time-lapse or 4D seismic data is unavailable or unreliable, such as in onshore reservoirs. The resultant processing results provide quantitative information for history matching purposes using a probabilistic approach to take in account uncertainties in the geological model and reduce uncertainties in reservoir production forecasts.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to history matching in petroleum reservoirsimulations, and more particularly obtaining information about changesin fluid displacement in reservoirs of onshore fields where surfacetime-lapse seismic surveys cannot be readily performed.

2. Description of the Related Art

Generating accurate production forecasts is an area of major concern forthe oil industry. Using uncertain production and reserves forecasts forinvestment decisions leads to a significant risk of sub-optimalperformance. It is difficult and expensive to generate consistent modelsto accurate represent oil fields due to geological complexities, thesize of the reservoir model, and the amount of data being produced. Fora large reservoir, such as the type known in the industry as a giantreservoir, the number of grid cells can often exceed hundreds ofmillions. This number of cells is required in order to have adequateresolution to represent flow dynamics, formation rock porosity andpermeability heterogeneity, and many other geologic and depositionalcomplexities within the reservoir. Needless to say, a reservoir model isa complex dynamic system.

Regardless of the stage of development of a field, its representation isequally challenging. A new field starting production has limited amountsof data. Traditionally, few wells are put to production in the earlystages of development. Thus, little information is known, and a reliablereservoir model can only be properly built after several years ofproduction data are acquired.

For a mature reservoir, on the other hand, there is a vast amount ofdata which presents a challenge to a reservoir engineer. A maturereservoir can have in excess of a hundred producing wells, millions ofactive grid cells and production data gathered over many decades.

Usually, present reservoir studies start by the acquisition of 3Dseismic data at the early stages of development and appraisal to obtaina clear picture of the field. This dataset is used to give theexploration and production teams a wider view of the field, reducingdevelopment uncertainties, and providing a better understanding of howto develop the field for optimum production. Only few wells are usuallydrilled in early stages, due to economic constrains. This provides alimited amount of information about the petrophysical properties of therocks, pressure, saturation, rock composition and fluid composition,which are only known at the well locations. These limited amounts ofinformation are used to create a first reservoir model. The model is notstatic and it is continuously updated as more information becomesavailable through a process known as history matching.

History matching is an important tool to obtain more accurate models todescribe the reservoir, thus improving the capability of producingaccurate forecasts. This is highly related to good reservoir managementpractices. Until recently, history matching was done by updating thereservoir model parameters to match historical production data. This wasoften an underdetermined inverse problem with multiple solutions.Different models might fit the given production data regardless ofwhether or not they were geologically accurate.

During the production stage from wells in a reservoir, not only the oilproduction rate (OPR) is measured, the gas oil rate (GOR) and the watercut (WCT) are also measured as these are important measures. The oilproduction rate represents the gross revenue obtainable, while high GORand WCT measures indicate factors which reduce potential income.

Fluid samples and the static bottomhole pressure (SBHP) are alsomeasured at selected wells during production to ensure consistency withthe development plan and simulations being carried out. The measuredpressure contains information about the reservoir continuity, fluidcontacts and its depletion mechanism. These parameters are taken intoconsideration during the history matching process.

Conventional history matching was designed as a trial and error processmaking it a complex and time consuming task. Considerable investment hasbeen made in recent years to improve history matching practices.Computer-assisted methods have been under development to help reservoirengineers explore new complex geological areas and to efficiently dealwith ever-increasing amounts of data being produced.

Among the most successful methods employed to condition reservoir modelsto production data are conjugate gradient optimization methods andensemble based Bayesian filtering methods. Conjugate gradient methodsrequire the calculation of the gradient of an objective functionmeasuring the model fit with the data. This is a challenging taskbecause it requires developing and running the adjoint code of thereservoir model.

A recent advancement in history matching is the use of time-lapseseismic data to help understand the fluid displacement in the reservoir.Time-lapse seismic data, also known as 4D seismic data, provides morespatial coverage than other reservoir data sets. Time-lapse seismic or4D seismic data have been used with success in the oil industry toimprove reservoir understanding, which in turn has great importance forreservoir management applications. The qualitative use of 4D seismic inits simplest form allows the identification of undrained areas “hotspots”, allowing reservoir engineers to properly design bettermanagement practices to improve oil recovery.

4D seismic surveying is performed by repeatedly shooting 3D seismicsurveys with arrays of closely spaced receivers and shot lines at thesurface over the same area at different times. The infill fluids presentin the reservoir rocks have different acoustic impedances. Thedifference between two seismic surveys over time indicated by changes ofacoustic impedance can then be used to highlight unexplored compartmentsand track movements of flood fronts.

Qualitative approaches have been implemented in the past decade to use4D seismic data sets, allowing development possibilities includingbetter well placement and fluid drainage. The use of more sophisticatedquantitative approaches has recently become possible. However, becauseof the nature and complexity of the data, which can exceed by severalorders of magnitude the multiple millions of grid cells in a largereservoir, most of the research performed so far only dealt withinverted seismic data for elastic parameters, mainly acoustic impedanceand Poisson's ratio. Other seismic and elastic attributes were at timesalso used.

To be considered a good candidate for a time-lapse study the analyzeddata needs to show significant variation over production activity.Density variations due to fluid saturation changes are minimal, usuallyin the range of 1%, thus they cannot be accounted for due to noise anduncertainty levels. The major variation occurs in the velocity field andconsequently bulk modulus of the rocks.

Other studies have tested alternative approaches to include time-lapseseismic in history matching studies. One approach was to directlyassimilate seismic data, before inversion and in amplitude form. J. A.Skjervheim and B. O. Ruud, Combined Inversion of 4D Seismic WaveformData And Production Data Using Ensemble Kalman Filter, 2006. A similarapproach extended this to a 3D reservoir. O. Leeuwenburgh, J. Brouwer,and M. Trani, Ensemble-Based Conditioning Of Reservoir Models To SeismicData, Computational Geosciences, 2011, 15(2): p. 359-378. Anotherapproach assimilated reparameterized seismic data in terms of arrivaltimes at the interpreted fluid fronts. M. Trani, R. Arts, and O.Leeuwenburgh, Seismic History Matching of Fluid Fronts Using theEnsemble Kalman Filter, SPE Journal, 2013, 18(1): p. 159-171.

In addition to the processing complexities above for reservoirs ingeneral, the technology of time lapse seismic data acquisition facesmajor challenges in onshore fields. In onshore fields, it is almostimpossible in most cases to acquire time-lapse data. This occurs mainlybecause changes in the surface environment (construction of surfacefacilities, urban expansion, alterations in the environment and otherreproducibility issues). These changes over time in the surfaceenvironment become part of the data content of the 4D surveys, and thusprevent observing differences between 4D seismic surveys to monitorreservoir performance. This is a primary reason that many oil producingcompanies do not have 4D seismic data for their onshore oil fields.

SUMMARY OF THE INVENTION

Briefly, the present invention provides a new and improved method ofhistory matching a reservoir model of an onshore reservoir producinghydrocarbon fluids from wells in the reservoir based on actualproduction from the reservoir over time and reservoir formationattribute data. A crosswell seismic survey is conducted between wells inthe reservoir, and data from the crosswell seismic survey processed in acomputer to obtain data about the reservoir formation attribute. Anupdated value of the reservoir formation attribute is determined in thecomputer, and the updated value of the reservoir formation attributeprovided to adjust the reservoir model in the computer.

The present invention also provides a new and improved computerimplemented method of history matching a reservoir model of an onshorereservoir producing hydrocarbon fluids from wells in the reservoir basedon actual production from the reservoir over time and reservoirformation attribute data based on results of a crosswell seismic surveyconducted between wells in the reservoir. Data from the crosswellseismic survey is processed in the computer to obtain data about thereservoir formation attribute, and an updated value determined of thereservoir formation attribute. The determined updated value of thereservoir formation attribute is provided by the computer to adjust thereservoir model.

The present invention also provides a new and improved data processingsystem for history matching a reservoir model of an onshore reservoirproducing hydrocarbon fluids from wells in the reservoir based on actualproduction from the reservoir over time and reservoir formationattribute data based on results of a crosswell seismic survey conductedbetween wells in the reservoir. The data processing includes a processorwhich processes data from the crosswell seismic survey to obtain dataabout the reservoir formation attribute, and determines an updated valueof the reservoir formation attribute. The processor provides the updatedvalue of the reservoir formation attribute to adjust the reservoirmodel.

The present invention also provides a new and improved data storagedevice which has stored in a non-transitory computer readable mediumcomputer operable instructions for causing a data processing system toperform history matching a reservoir model of an onshore reservoirproducing hydrocarbon fluids from wells in the reservoir based on actualproduction from the reservoir over time and reservoir formationattribute data based on results of a crosswell seismic survey conductedbetween wells in the reservoir. The instructions stored in the datastorage device cause the processors to process data from the crosswellseismic survey to obtain data about the reservoir formation attribute,and determine an updated value of the reservoir formation attribute. Theinstructions also cause the processor to provide the updated value ofthe reservoir formation attribute to adjust the reservoir model.

The present invention also provides a new and improved computerimplemented method of history matching a reservoir model based onproduction data from an onshore reservoir and reservoir formationattribute data acquired from base crosswell seismic surveys betweenwells in the reservoir at a select time during production. A number ofpotential geological ensembles for the formation attributes are formedbased on the reservoir model in its present state, and iteration in timeis made to a time of a most recent reservoir model. The reservoirformation attribute data is updated based on production data prior tothe most recent reservoir model, and the reservoir model updated withthe updated reservoir formation attribute data. A time increment isadvanced from the time of the most recent reservoir model. At theadvanced time increment a crosswell survey is determined for the numberof potential geological ensembles using the updated reservoir model. Atravel time lapse difference is determined for the crosswell surveys forthe number of potential geological ensembles, and the potentialgeological ensemble with a travel time lapse most close to that of themost recent reservoir model determined at the advanced time increment.The reservoir model is updated with the formation attributes of thepotential geological ensemble with a travel time lapse most close tothat of the most recent base crosswell seismic survey.

The present invention also provides a new and improved data processingsystem for history matching a reservoir model based on production datafrom an onshore reservoir and reservoir formation attribute dataacquired from base crosswell seismic surveys between wells in thereservoir at a select time during production. Based on the instructionsstored in the data storage device, a number of potential geologicalensembles for the formation attributes are formed by a processor in thedata processing system based on the reservoir model in its presentstate, and iteration in time is made to a time of a most recentreservoir model. The reservoir formation attribute data is updated bythe processor based on production data prior to the most recentreservoir model, and the reservoir model updated with the updatedreservoir formation attribute data. A time increment is advanced in theprocessor from the time of the most recent reservoir model. At theadvanced time increment a crosswell survey is determined by theprocessor for the number of potential geological ensembles using theupdated reservoir model. A travel time lapse difference is determined inthe processor for the crosswell surveys for the number of potentialgeological ensembles, and the potential geological ensemble with atravel time lapse most close to that of the most recent reservoir modeldetermined at the advanced time increment. The reservoir model isupdated by the processor with the formation attributes of the potentialgeological ensemble with a travel time lapse most close to that of themost recent base crosswell seismic survey.

The present invention also provides a new and improved data storagedevice which has stored in a non-transitory computer readable mediumcomputer operable instructions for causing a data processing system toperform history matching a reservoir model based on production data froman onshore reservoir and reservoir formation attribute data acquiredfrom base crosswell seismic surveys between wells in the reservoir at aselect time during production. A number of potential geologicalensembles for the formation attributes are formed based on the reservoirmodel in its present state, and iteration in time is made to a time of amost recent reservoir model. The reservoir formation attribute data isupdated based on production data prior to the most recent reservoirmodel, and the reservoir model updated with the updated reservoirformation attribute data. A time increment is advanced from the time ofthe most recent reservoir model. At the advanced time increment acrosswell survey is determined for the number of potential geologicalensembles using the updated reservoir model. A travel time lapsedifference is determined for the crosswell surveys for the number ofpotential geological ensembles, and the potential geological ensemblewith a travel time lapse most close to that of the most recent reservoirmodel determined at the advanced time increment. The reservoir model isupdated with the formation attributes of the potential geologicalensemble with a travel time lapse most close to that of the most recentbase crosswell seismic survey.

BRIEF DESCRIPTION OF THE DRAWINGS

The application file contains at least one drawing executed in color.Copies of this patent application publication with color drawings willbe provided by the Patent and Trademark Office upon request and paymentof the necessary fee.

FIG. 1 is a surface diagram of source wells and receiver wells for acrosswell seismic data survey.

FIG. 2 is a schematic diagram, taken in cross-section, of a crosswellseismic data survey between a source well and a receiver well.

FIG. 3 is a schematic diagram of history matching of reservoirproduction and time-lapse seismic data.

FIG. 4 is a schematic diagram of history matching of time-lapsecrosswell seismic data using ensemble Kalman filtering according to thepresent invention.

FIG. 5 is a functional block diagram of a flow chart of data processingsteps for history matching of time-lapse crosswell seismic data usingensemble Kalman filtering according to the present invention.

FIG. 6 is a schematic diagram of a computer network for history matchingof time-lapse crosswell data using ensemble Kalman filtering accordingto the present invention.

FIG. 7 is a display of a porosity field used as a model for processingaccording to the present invention.

FIG. 8 is a display of a permeability field used as a model forprocessing according to the present invention.

FIG. 9 is a histogram for the porosity model of FIG. 7.

FIG. 10 is a histogram for the permeability model of FIG. 8.

FIG. 11 is a plot of the data correlation between the porosity field ofFIG. 7 and the permeability field of FIG. 8.

FIG. 12 is a plot of potential cumulative oil production from a modelreservoir for various possible porosities and permeabilities.

FIG. 13 is a plot of potential production plateau duration from a modelreservoir for various possible porosities and permeabilities.

FIG. 14 is a plot showing the potential cumulative oil production from amodel reservoir for various possible porosities and permeabilities basedon the assimilation of production data.

FIG. 15 is a plot showing the potential production plateau duration froma model reservoir for various possible porosities and permeabilitiesbased on the assimilation of production data.

FIG. 16 is a plot of the estimated porosity distribution obtained withthe assimilation of production data and in accordance with the presentinvention.

FIG. 17 is a plot of the estimated permeability distribution obtainedwith the assimilation of production data and in accordance with thepresent invention.

FIG. 18 is a plot showing the potential cumulative oil production from amodel reservoir for various possible porosities and permeabilities basedon the joint assimilation of production and time-lapse acousticimpedance data.

FIG. 19 is a plot showing the potential production plateau duration froma model reservoir for various possible porosities and permeabilitiesbased on the joint assimilation of production and time-lapse acousticimpedance data.

FIG. 20 is a plot of the estimated porosity distribution obtained withthe assimilation of production and acoustic impedance data and inaccordance with the present invention.

FIG. 21 is a plot of the estimated permeability distribution obtainedwith the assimilation of production and acoustic impedance data and inaccordance with the present invention.

FIG. 22 is a plot showing the potential cumulative oil production from amodel reservoir for various possible porosities and permeabilities basedon the joint assimilation of production and time-lapse crosswell data.

FIG. 23 is a plot showing the potential production plateau duration froma model reservoir for various possible porosities and permeabilitiesbased on the joint assimilation of production and time-lapse crosswelldata.

FIG. 24 is a plot of the estimated porosity distribution obtained withthe assimilation of production and crosswell data and in accordance withthe present invention.

FIG. 25 is a plot of the estimated permeability distribution obtainedwith the assimilation of production and crosswell data and in accordancewith the present invention.

FIG. 26 is a plot showing the potential cumulative oil production from amodel reservoir for various possible porosities and permeabilities basedon the joint assimilation of production and time-lapse zero-offsettravel-time crosswell data.

FIG. 27 is a plot showing the potential production plateau duration froma model reservoir for various possible porosities and permeabilitiesbased on the joint assimilation of production and time-lapse zero-offsettravel-time crosswell data.

FIG. 28 is a plot of the RRMS error for the estimated porosity based onthe production data, joint assimilation of production and seismicimpedance data joint assimilation of production and crosswell time-lapsevelocity data and in accordance with the present invention.

FIG. 29 is a plot of the RRMS error for the estimated permeability basedon the production data, joint assimilation of production and seismicimpedance data joint assimilation of production and crosswell time-lapsevelocity data and in accordance with the present invention.

FIG. 30 is a plot showing the potential cumulative oil production from amodel reservoir for various possible porosities and permeabilities basedon the joint assimilation of production and time-lapse crosswell data.

FIG. 31 is a plot showing the potential production plateau duration froma model reservoir for various possible porosities and permeabilitiesbased on the joint assimilation of production and time-lapse crosswelldata.

FIG. 32 is a comparison plot of porosity estimate improvement obtainedwith time-lapse acoustic impedance data and with crosswell time-lapseseismic survey data using high frequency waves according to the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Crosswell SeismicSurveying

With the present invention, it has been found that crosswell seismicdata can be used as a source of time-lapse information for processingaccording to the present invention to provide information for reservoiranalysts and engineers regarding fluid displacement within a reservoir.The crosswell seismic data is also more reproducible than currenttechniques (4D seismic), requires less time to be acquired and has lowerdata acquisition costs when compared to 4D seismic.

FIG. 1 indicates schematically a map of the relative locations of agroup of wells W, including an injector well I and four producer wells Pinvolved in the production of oil from a subsurface reservoir R (FIG.2). During a crosswell seismic survey, a seismic source line 30 islowered by wireline in a borehole 32 of one of the wells W to a selecteddepth or depths of interest relating to the reservoir R. A receiverarray 34 of receivers or geophones 35 is also lowered in a borehole 36of other adjacent wells W.

The sources 30 are activated generating seismic impulses that propagatealong the interwell region through the reservoir R. The seismic impulsesignal is captured after travel through the interwell region by thereceivers 35 in the adjacent wells W. An initial survey or base surveyis made before production has begun is from the reservoir R.

As indicated by arrows 38 in FIG. 1, for the purpose of the presentinvention, time lapse data is acquired for each pair of adjacent wellsW: between the injector well I and the producer wells P, and betweeneach of the adjacent pairs of producer wells P.

Thus travel-time information for the interwell region is recorded. Theinterwell travel time information is then processed with what is knownas crosswell tomographic processing in a computer or data processingsystem such as D (FIG. 6) to yield data or information about formationproperties and acoustic velocity in the reservoir R.

A further acquisition of crosswell seismic data for the wells W isperformed in a monitor crosswell seismic survey after sufficient timehas elapsed so there is enough fluid displacement in the field such thata significant difference in the time-lapse signal can be measured.Further monitor surveys are taken at comparable time intervals duringproduction from the reservoir R. This data is used, as will bedescribed, during the history matching process to better constrainporosity and permeability distributions.

The difference between the monitor and the base surveys after suitableprocessing provides information about the fluid properties in thisregion and can be used to improve the quality of the simulation modelbeing used to forecast production for this reservoir.

Crosswell seismic data provides what are known as P and S wave data thatcan be used to compute velocity tomograms. The velocity changes can thenbe mapped over time and linked to fluid displacement in the reservoir.This provides a smaller data coverage area, but avoids reproducibilityissues especially in onshore fields were time-lapse data is still amajor challenge. Time-lapse surveys cannot be conducted in many onshorefields due to surface limitations which could for instance happen afteran urban expansion and/or some changes in the environment.

Typically surface seismic applications use low frequencies (in the rangeof 0 to 100 Hz). The major reason for this limited range of frequenciesis the fact that high frequencies are more attenuated, which limits themaximum distance than can be imaged. With the present invention, thecrosswell tomographies obtained from the crosswell surveys providetransmission images in which sources and receivers are opposite to eachother, thus the attenuation is less intense than in the conventionalsurface seismic surveys where the seismic waves need to travel throughthe overburden and back again. Typical frequencies used in crosswellimages are in the range of few hundred Hz. At higher acquisitionfrequencies the velocity dispersion phenomena delivers valuableinformation about the fluid content in the media. This may not beproperly modeled using the Gassman fluid displacement currently used inreservoir modeling. According to the present invention, a Biot velocitymodel can be used, as will be explained below, to predict elasticproperties at the high frequency limit.

Crosswell tomographies are presently used in enhanced oil recovery (EOR)applications by steam injection to track the flooding process due totemperature variations and CO₂ injection. However the approach used sofar is qualitative, and a more sophisticated approach is required toretrieve as much information as possible about the fluid displacementinside the reservoir. Some quantitative uses for this type of data havebeen attempted. Liang, et al., Improved Estimation of Permeability fromJoint Inversion of Time-Lapse Crosswell Electromagnetic and ProductionData Using Gradient-Based Method in SPE Annual Technical Conference andExhibition, 2011, used crosswell electromagnetic and production data toestimate permeability in a synthetic model using iterative Gauss-Newtonoptimization. Liang, et al, Joint Inversion Of Time-Lapse CrosswellSeismic And Production Data For Reservoir Monitoring AndCharacterization, 6th International Petroleum Technology Conference,2013, used the same methodology to incorporate inverted seismic andproduction data using wave form inversion. Both studies use gradientbased methods which are not suitable for highly non-linear and complexmodels for which the Ensemble Kalman Filtering with the presentinvention may provide accurate estimates at a fraction of thecomputational cost and implementation efforts.

NOMENCLATURE OPR = Oil Production Rate WCT = Water Cut BHP = Bottomholepressure SBHP = Static Bottomhole pressure GOR GOR = Gas Oil Rate RRMS =Relative Root Mean Square Error PDF = Probability Density Function EnKF= Ensemble Kalman Filter STD = Standard Deviation V_(p) = PrimaryVelocity V_(s) = Shear Velocity KF = Kalman Filter K_(dry) = BulkModulus Dry Rock K_(sat) = Bulk Modulus Saturated Rock K_(fluid) = BulkModulus Fluid K_(s) = Bulk Modulus Rock Matrix G_(dry) = Shear ModulusDry Rock G_(Sat) = Shear Modulus Saturated Rock ρ_(sat) = DensitySaturated Rock I_(P) = Seismic Impedance ν = Poisson's Ratio ϕ =Porosity ϕ_(c) = Critical Porosity S_(w) = Water Saturation M =Dynamical Model Forward Operator η = Noise x = Ensemble Average{circumflex over (P)} = Covariance Matrix {circumflex over (K)} = KalmanGain H = Linear Measurement Operator

History Matching

A high level version of the workflow for history matching of productionand time lapse data according to the present invention is shown in FIG.3. The processing is an iterative process that evolves in time as moreinformation about reservoir production over time becomes available.

The first step in this workflow as indicated by step 40 is theutilization of the previous parameters and states estimates (porosity,permeability, saturation and pressure) to perform the reservoirsimulations, i.e., a set of reservoir models is established. A crosswellbaseline survey is acquired in the manner described above regardingFIGS. 1 and 2 is stored for future use. Then the simulations areforwarded in time to predict future reservoir performance as indicatedby step 44. Based on the most updated reservoir states at the end of thepredicted period (saturation and pressure) and the reservoir parameters(porosity and saturation) a monitor survey is computed as indicated bystep 42 also in the manner described above regarding FIGS. 1 and 2. Thetime-lapse difference (difference between the monitor and the basesurvey) is then computed and used side by side with the predictedreservoir performance (WCT, WOPR, WBHP) during step 46 to update theearlier reservoir model estimates, as well as to serve as a startingpoint for the next time iteration of history matching. The workflow isshown in more details as a flow chart F in FIG. 5 and described below.

The history matching process is performed by the data processing systemD (FIG. 6) operating according to the present invention. To efficientlyincorporate crosswell data in the reservoir history matching workflowthree components of the processing done by the data processing system Dare utilized, as will be described: a Reservoir Simulator R, aPetro-Elastic Module M and a History Matching Module H.

The present invention provides quantitative incorporation of theproduction and time-lapse dataset in the history matching process. Withthe present invention, an automated history matching tool incorporatingEnsemble Kalman Filtering is provided so that better estimates porosityand permeability fields are available for the history matching process.

The History Matching Module H is the primary component for processingaccording to the present invention. The History Matching Module Hinteracts with the Reservoir Simulator R and Petro-Elastic Module M toprovide an improved history matched solution of predicted reservoirproduction. The History Matching Module H uses several geologicalrealizations to account for the uncertainties in the initial modelthrough a probabilistic approach.

A baseline or base crosswell survey is initially acquired beforeproduction is begun in the reservoir as indicated at step 42 (FIG. 3),and subsequent crosswell surveys performed later during production toquantify the fluid displacement in the reservoir R. The time-lapsedifference (difference between the initial or monitor survey and thesubsequent ones) is used by the History Matching Module H to improve thequality of the match between actual production and reservoir simulation,and thus reduce the uncertainty in the porosity and permeability fields.

With the present invention, fluid displacement information is providedas a result of the processing from time-lapse data at a fraction of thecurrent 4D data acquisition cost. Further, quantitative use of crosswelltime-lapse velocity data mapped by a crosswell tomography andassimilated is provided using the EnKF filtering, as will be discussed,during processing as a substitute for 4D seismic.

Processing Analytics

The methodology of the present invention modifies the Petro-ElasticModule M and the History Matching Module H of the data processing systemD. The Gassmann's equations in a conventional Petro-Elastic Module M arereplaced according to the present with more representative formulas topredict the seismic impedance at higher frequencies. These formulas areBiot's velocity model and or the viscoelasticity model. ThePetro-Elastic Module M is used to predict the seismic impedance and/orvelocity of the grid cells of the reservoir being imaged by thecrosswell tomography. The predicted values of seismic impedance orvelocity, or both, are based on the current simulation properties(porosity, pressure, fluid content, density, saturation and the like) ofthe reservoir as a result of step 44.

In the History Matching Module H, the time-lapse data attributedifference for each grid cell within the region being imaged isassimilated using the Ensemble Kalman Filter technique. Ensemble KalmanFiltering is a Bayesian filtering technique in which an ensemble ofgeological realizations is updated as data becomes available leading toimproved estimates of the initial conditions (in this case porosity andpermeability). By using production and crosswell data together toimprove the porosity and permeability estimates, comparable results canbe obtained to those from conventional history matching of productionand usually unavailable and more expensive 4D seismic data.

The Petro-Elastic Module M describes the rock physics which essentiallyrepresent the link between reservoir engineering and geophysics,connecting seismic data to the presence of in situ hydrocarbons and toreservoir characteristics. The model utilized in the Petro-ElasticModule M is composed of a set of equations used to calculate bulkmodulus, P and S impedance from simulated pressure, fluid saturation,porosity and fluid content data.

The most general equations are the Batzle and Wang equations for thefluid properties and the Gassmann's equations for rock properties. Theserelations predict elastic properties of saturated porous medium fromsimulated fluid and static rock properties creating a bridge betweenfluid flow and wave propagation domains. The most widely used method fordetermining the effects of production induced fluid change is theGassmann substitution method described by Equations (12) and (13) below.The Gassmann substitution method predicts the increase in the effectivebulk modulus K_(Sat) and shear modulus of the saturated rock G_(sat)based on the porosity φ and bulk modulus of the dry rock K_(dry), fluidK_(fluid), effective density ρ_(sat), rock matrix K_(S) and shearmodulus of the dry rock G_(dry).

However, as explained above, the Gassman fluid displacement model neednot be used with the present invention. Rather, it has been found thatthe Biot velocity model may be used and take advantage of the dataavailable at higher frequencies from crosswell seismic surveys accordingto the present invention.

As explained by Mavko, G., Mukerji, T., Dvorkin, J. 2009, The RockPhysics Handbook: Tools For Seismic Analysis Of Porous Media, CambridgeUniversity Press, Biot modeling derives the theoretical formulas forpredicting velocities changes in saturated rocks. This formulationincorporates some but not all the mechanisms of viscous and inertialinteraction between the pore fluid and the mineral matrix of the rock.In contrast to Gassmann's equations, the Biot velocity model predictsfrequency dependent velocity components, while Gassmann modelingpredicts only the low frequency component.

The equations describing Biot's model are given by:

$\begin{matrix}{V_{P{({{fast},{slow}})}} = \left\lbrack \frac{\Delta \pm \left\lbrack {\Delta^{2} - {4{S\left( {{PQ} - R^{2}} \right)}}} \right\rbrack^{\frac{1}{2}}}{2S} \right\rbrack^{1/2}} & {{Equation}\mspace{14mu}(1)} \\{V_{S} = \left( \frac{G_{dry}}{\rho - {{\phi\rho}_{fl}\alpha^{- 1}}} \right)} & {{Equation}\mspace{14mu}(2)} \\{\Delta = {{P\;\rho_{22}} + {R\;\rho_{11}} - {2Q\;\rho_{12}}}} & {{Equation}\mspace{14mu}(3)} \\{P = \frac{{\left( {1 - \phi} \right)\left( {1 - \phi - \frac{K_{dry}}{K_{S}}} \right)K_{S}} + {\phi\;\frac{K_{S}K_{dry}}{K_{fluid}}}}{1 - \phi - \frac{K_{dry}}{K_{S}} + {\phi\;\frac{K_{S}}{K_{fluid}}}}} & {{Equation}\mspace{14mu}(4)} \\{Q = \frac{\left( {1 - \phi - \frac{K_{dry}}{K_{S}}} \right)\phi\; K_{S}}{1 - \phi - \frac{K_{dry}}{K_{S}} + {\phi\;\frac{K_{S}}{K_{fluid}}}}} & {{Equation}\mspace{14mu}(5)} \\{R = \frac{\phi^{2}\; K_{S}}{1 - \phi - \frac{K_{dry}}{K_{S}} + {\phi\;\frac{K_{S}}{K_{fluid}}}}} & {{Equation}\mspace{14mu}(6)} \\{S = {{\rho_{11}\rho_{22}} - \rho_{12}^{2}}} & {{Equation}\mspace{14mu}(7)} \\{\alpha = {1 - {r\left( {1 - \frac{1}{\phi}} \right)}}} & {{Equation}\mspace{14mu}(8)} \\{\rho_{11} = {{\left( {1 - \phi} \right)\rho_{0}} - {\left( {1 - \alpha} \right){\phi\rho}_{fl}}}} & {{Equation}\mspace{14mu}(9)} \\{\rho_{22} = {\alpha\phi\rho}_{fl}} & {{Equation}\mspace{14mu}(10)} \\{\rho_{12} = {\left( {1 - \alpha} \right){\phi\rho}_{fl}}} & {{Equation}\mspace{14mu}(11)}\end{matrix}$where K_(dry) is the effective bulk modulus of the rock frame (dryframe) and G_(dry) the shear modulus, K_(fluid) is the bulk modulus ofthe pore fluid, K_(S) is the bulk modulus of the rock mineral, ρ₀ is themineral density, ρ_(f1) the fluid density, r is a geometrical factorassociated with the shape of the pores and a is a parameter accountingfor the rock and fluid coupling, called tortuosity. The fast highfrequency wave is most easily observed in the lab and in the field itrepresents the compressional body wave.

Gassmann's equations agree with Biot's formulation for the low frequencycase. The Gassmann's equations are:

$\begin{matrix}{K_{sat} = {K_{dry} + \frac{\left( {1 - \frac{K_{dry}}{Ks}} \right)^{2}}{\frac{\phi}{K_{fluid}} + \frac{1 - \phi}{K_{s}} - \frac{K_{dry}}{K_{s}^{2}}}}} & {{Equation}\mspace{14mu}(12)} \\{G_{sat} = G_{dry}} & {{Equation}\mspace{14mu}(13)} \\{V_{P} = \left\lbrack \frac{K_{sat} + {\frac{4}{3}G_{sat}}}{\rho_{sat}} \right\rbrack^{1/2}} & {{Equation}\mspace{14mu}(14)} \\{I_{P} = {\rho_{sat}V_{P}}} & {{Equation}\mspace{14mu}(15)}\end{matrix}$

Ensemble Kalman Filtering

To provide better estimates of porosity and permeability the initialensemble previously created is conditioned according to the presentinvention with historical data and model dynamics over time. This isdone using Ensemble Kalman filtering.

The Ensemble Kalman Filtering (EnKF) according to the present provides aset of geological realizations which are generated to take in accountthe uncertainties in the geological model. This set of realizations isforwarded in time and corrected dynamically as production and time-lapsedata becomes available. For each realization, the predicted reservoirperformance and time-lapse response is generated as the output of theReservoir Simulator Module R and the Petro-Elastic Module M. Thepredicted reservoir performance and time-lapse response is used duringthe EnKF processing to estimate a covariance matrix. The production data(true reservoir performance) and time-lapse data obtained from the fieldare used to correct states of the realizations as they are formed.Consequently the forecast values generated by these realizations becomecloser to the observed values.

The ensemble Kalman filter (EnKF) was first introduced by Evensen.Evensen, G., Sequential Data Assimilation With A NonlinearQuasi-Geostrophic Model Using Monte Carlo Methods To Forecast ErrorStatistics, Journal of Geophysical Research: Oceans (1978-2012), 1994,99(C5): p. 10143-10162. EnKF's are Monte Carlo based techniques thatstochastically generate models which are integrated in time to estimatethe prior probability density functions (or pdfs). What is known as theBayes rule is then used to update the prior pdf to the posterior pdfwith most recent data. This updating can be implemented independently ofa reservoir simulator with reasonable computational requirements, makingit an appealing choice for this reason. This methodology can besuccessfully applied to history matching, producing promising results,often superior as described below to those obtained with conventionalhistory matching methods.

The Ensemble Kalman filter (EnKF) has an additional advantage. Bygenerating an ensemble of realizations and propagating them in time, anerror estimate about the forecast can be obtained providing additionalinformation to the decision maker.

The EnKF uses a sample or ensemble of state vectors, Equation (16),where N_(e) denotes the number of ensemble members. At every forecaststep, all ensemble members are integrated forward in time with thereservoir model represented by Equation (17). The state estimate and theassociated covariance matrix are respectively estimated using Equation(18) and Equation (19).

$\begin{matrix}\left\{ {x^{i},{= 1},2,\ldots\mspace{14mu},N_{e}} \right\} & {{Equation}\mspace{14mu}(16)} \\{x_{k}^{f,i} = {{\mathcal{M}_{{k - 1},k}\left( x_{k - 1}^{a,i} \right)} + \eta_{k}^{i}}} & {{Equation}\mspace{14mu}(17)} \\{{\overset{\_}{x}}_{k}^{f} = {\frac{1}{N_{e}}{\sum\limits_{i = 1}^{N_{e}}x_{k}^{f,i}}}} & {{Equation}\mspace{14mu}(18)} \\{{\hat{P}}_{k}^{f} = {\frac{1}{N_{e} - 1}{\sum\limits_{i = 1}^{N_{e}}{\left( {x_{k}^{f,i} - {\overset{\_}{x}}_{k}^{f}} \right)\left( {x_{k}^{f,i} - {\overset{\_}{x}}_{k}^{f}} \right)^{T}}}}} & {{Equation}\mspace{14mu}(19)}\end{matrix}$

The sample covariance can be written as in Equation (20), where thei^(th) column of X_(k) ^(f) is

$\left( {N_{e} - 1} \right)^{- \frac{1}{2}}{\left( {x_{k}^{f,i} - {\overset{\_}{x}}_{k}^{f}} \right).}$The analysis step is performed using the linear Kalman Filter (KF)update Equation (21) where {circumflex over (K)}_(k) is theensemble-based approximate Kalman gain at t_(k), y_(k) ^(i) is theobservation perturbed with noise sampled from the distribution of theobservational error given by Equation (22).{circumflex over (P)} _(k) ^(f) =X _(k) ^(f)(X _(k) ^(f))^(T)  Equation(20)X _(k) ^(a,i) =X _(k) ^(f,i) +{circumflex over (K)} _(k) [y _(k) ^(i) −H_(k) x _(k) ^(f,i)]  Equation (21){circumflex over (K)} _(k) =X _(k) ^(f)(H _(k) X _(k) ^(f))^(T)[(H _(k)X _(k) ^(f))(H _(k) X _(k) ^(f))^(T) +R _(k)]⁻¹  Equation (22)

The analysis state and its covariance matrix are then expressed byEquation (23) and Equation (24), respectively.

$\begin{matrix}{{\overset{\_}{x}}_{k}^{a} = {\frac{1}{N_{e}}{\sum\limits_{i = 1}^{N_{e}}x_{k}^{a,i}}}} & {{Equation}\mspace{14mu}(23)} \\{{\hat{P}}_{k}^{a} = {\frac{1}{N_{e} - 1}{\sum\limits_{i = 1}^{N_{e}}{\left( {x_{k}^{a,i} - {\overset{\_}{x}}_{k}^{a}} \right)\left( {x_{k}^{a,i} - {\overset{\_}{x}}_{k}^{a}} \right)^{T}}}}} & {{Equation}\mspace{14mu}(24)}\end{matrix}$

Porosity, permeability, saturation and pressure are included in thestate vector during processing according to the present invention.Porosity and permeability are static variables while pressure andsaturation are dynamic (produced by the reservoir simulator in runtime).The assimilated data is composed of production and seismic data obtainedfrom the original model perturbed with Gaussian errors.

Processing Methodology

A flow chart F (FIG. 5) illustrates the basic computer processingsequence used in the history matching process according to the presentinvention and the computational methodology taking place during atypical embodiment of a history matching of time-lapse crosswell datausing Ensemble Kalman filtering according to the present invention.

During step 50, an initial estimate of several possible realizations ofa reservoir model is formed. Next, during step 52, as part of thehistory matching with Ensemble Kalman filtering processing, thereservoir model realizations formed during step 50 are iteratedsequentially based on the production data gathered since the lastiteration. This is a conventional history match based on production dataalone as illustrated in FIG. 4.

The history match based on production data alone of FIG. 4 includesprocessing much like that described in FIG. 3, except no time lapse datais involved. Accordingly, the establishment of reservoir models step ofFIG. 4 bears a like reference numbered 40 to the comparable step of FIG.3 described above. Similarly, the forecasting or prediction step 44 ofFIG. 4 bears a like reference to the comparable step of FIG. 3 describedabove as is also the case for the step 46 of updating the reservoirmodel estimates.

During step 54, the reservoir simulation module R is restarted and theestimates of porosity and permeability are updated based on the resultsof step 52. In step 56, a set of base crosswell survey data is computedfor each ensemble member using the Petro-Elastic module M with theupdated porosity and permeability properties resulting from step 54.This dataset as well as the observed field data (time-lapse crosswellsurveys) are stored in memory.

During step 58, the Reservoir Simulator Module R is advanced in untilthe moment that the monitor survey was collected in the field. Duringstep 60, a monitor crosswell survey is computed for the presentreservoir simulator time step for each ensemble member. Step 62 involvesdetermining a time-lapse difference between the monitor crosswellseismic survey and the base crosswell seismic survey determined duringstep 60. The observed and simulated time-lapse differences areincorporated in the processing methodology as the relative differencebetween base and monitor survey as expressed by Equation (25).

$\begin{matrix}{{{Time} - {{lapse}\mspace{14mu}{difference}\mspace{14mu}(\%)}} = \frac{100\left( {{Monitor} - {Base}} \right)}{Base}} & {{Equation}\mspace{14mu}(25)}\end{matrix}$

During step 64, the time-lapse difference and the predicted reservoirperformed simulated for each ensemble member is then incorporated in thehistory matching loop by means of the Ensemble Kalman Filter (EnKF).

The observed data (reservoir performance and time-lapse data) isperturbed during step 64 with Gaussian errors by a user specifiedstandard deviation (STD). The square of these same values were used asgiven variances of the observational errors in the computation of thegain matrix in Equation (22), which were assumed uncorrelated (i.e., Rdiagonal). Then the Kalman gain matrix is computed taking as input thepredicted reservoir performance (WCT, WBHP, WOPR), time-lapse differencefor each ensemble member and covariance matrix as expressed by Equation(22). The Kalman gain is them used to update the state vector by meansof the Equation (21).

During step 66, the Reservoir Simulator Module R may be restarted, orpredictions of reservoir production can be made by the simulator basedon the most recent reservoir states and the updated Petro-Elastic ModelM. Data generated during step 66 is then stored in memory of the dataprocessing system D and also available for display and analysis by usersof the data processing system D.

Data Processing System

As illustrated in FIG. 6, the data processing system D includes acomputer 70 having a master node processor 72 and memory 74 coupled tothe processor 72 to store operating instructions, control informationand database records therein. The data processing system D may be amulticore processor with nodes such as those from Intel Corporation orAdvanced Micro Devices (AMD), an HPC Linux cluster computer or amainframe computer of any conventional type of suitable processingcapacity such as those available from International Business Machines(IBM) of Armonk, N.Y. or other source. The data processing system D mayalso be a computer of any conventional type of suitable processingcapacity, such as a personal computer, laptop computer, or any othersuitable processing apparatus. It should thus be understood that anumber of commercially available data processing systems and types ofcomputers may be used for this purpose.

The processor 72 is accessible to operators or users through userinterface 76 and is available for displaying output data or records ofprocessing results obtained according to the present invention with anoutput graphic user display 78. The output display 78 includescomponents such as a printer and an output display screen capable ofproviding printed output information or visible displays in the form ofgraphs, data sheets, graphical images, data plots and the like as outputrecords or images.

The user interface 76 of computer 70 also includes a suitable user inputdevice or input/output control unit 80 to provide a user access tocontrol or access information and database records and operate thecomputer 70. Data processing system D further includes a database 82 ofreservoir data and crosswell survey data stored in computer memory,which may be internal memory 74, or an external, networked, ornon-networked memory as indicated at 86 in an associated database server90.

The data processing system D includes program code 92 stored innon-transitory memory 94 of the computer 70. The program code 92according to the present invention is in the form of computer operableinstructions causing the data processor 70 to perform history matchingof time-lapse crosswell data using ensemble Kalman filtering accordingto the present invention in the manner that has been set forth.

The computer memory 74 also contains stored computer operatinginstructions in the non-transitory form of History Matching Module H,the Petro-Elastic Module M, the Reservoir Simulator Module R, and alsothe data from data base 82 being manipulated and processed by theprocessor 72.

It should be noted that program code 92 may be in the form of microcode,programs, routines, or symbolic computer operable languages that providea specific set of ordered operations that control the functioning of thedata processing system D and direct its operation. The instructions ofprogram code 92 may be stored in memory 74 of the data processing systemD, or on computer diskette, magnetic tape, conventional hard disk drive,electronic read-only memory, optical storage device, or otherappropriate data storage device having a computer usable non-transitorymedium stored thereon. Program code 92 may also be contained on a datastorage device such as server 90 as a non-transitory computer readablemedium, as shown.

The data processing system D may be comprised of a single CPU, or acomputer cluster as shown in FIG. 6, including computer memory and otherhardware that makes it possible to manipulate data and obtain outputdata from input data. A cluster is a collection of computers, referredto as nodes, connected via a network. Usually a cluster has one or twohead nodes or master nodes 72 that are used to synchronize theactivities of the other nodes, referred to as processing nodes 94. Theprocessing nodes 94 all execute the same computer program and workindependently on different segments of the grid which represents thereservoir.

Experimental Data

The following example based on synthetic data was built to compare thepotential of the method when compared with well-establishedmethodologies (4D seismic). An identical twin experiment intended forhistory matching purposes was used for this purpose.

The objective of this study is to reduce uncertainties in the cumulativeproduction forecast and duration of the production plateau. Theuncertainty in these circumstances is defined as the ensemble spread inthe cumulative production curve and duration of the production plateau.RRMS error reductions for porosity and permeability are also calculatedto investigate the quality of the estimates.

A two dimensional domain model formed of one horizontal layer of 40 by40 grid cells of dimension 50 by 50 meters. The thickness of the layeris 25 meters. The reservoir is composed of unconsolidated sandstone. Themodel uses water flooding as recovery strategy. The injection iscontrolled by voidage replacement. A five spot pattern comparable tothat shown in FIG. 1 is used to produce the reservoir (four producers ineach one of the corners and one injector in the center).

Only two phases are considered, water and oil. The initial conditionsare specified as equilibrium conditions for the simulator. Therefore,the simulator calculates the initial pressure distribution based on thepressure and the depth of the datum and oil contacts. The initialsaturation is assumed to be constant and equal to the connate wateralong the entire domain. The simulated fluid is treated as dead oil.

The geological properties (permeability and porosity) were populatedgeostatistically as seen in FIGS. 7 and 8. A high porosity and a highpermeability area is present as shown in FIGS. 7 and 8, respectively, inthe left side of the field while a lower permeability and porosity areais present in the lower right portion of the field. The attributes aredistributed approximately following a Gaussian distribution (FIGS. 9 and10). Permeability was obtained through co-kriging using the porosity assecondary parameter. Thus a correlation between porosity andpermeability is present in the geological model (FIG. 11). For thisparticular study MRST—(Matlab Reservoir Software Tool), an open sourcereservoir simulation toolbox developed by SINTEF was used.

The reservoir performance is evaluated for 16 years using numerical timesteps of 30 days. The parameters used to create the true model aresummarized in the Table 1.

TABLE 1 Summary Of The Properties Used To Build The Reservoir ModelProperty Value Pressure (Reference) 30 MPa Oil density 859 Kg/m³ Waterdensity 1014 Kg/m³ Viscosity water 0.4 cP Viscosity oil 0.9 cP Connatewater 0.2 Irreducible oil saturation 0.2 Water injection rate 2000m³/day Relative permeability 1 

Porosity, saturation, density of the fluids and rocks forecast by thesimulator or obtained from the geological model are used to calculateseismic attributes. The petrophysical constants employed in thesimulation where obtained from M. Holmes and A. Holmes (2005),Petrophysical Rock Physics Modeling: A Comparison Of The Krief andGassmann Equations, and Applications To Verifying and EstimatingCompressional and Shear Velocities, presented at the 46^(th) AnnualLogging Symposium, SPWLA 46th Annual Logging Symposium, New Orleans:Society of Petroleum Well Log Analysts. The bulk modulus of the matrixrock is K_(s)=37.9 GPa and shear modulus G_(s)=44 GPa. The bulk modulusof water and gas are K_(water)=3.05 GPa and K_(oil)=0.43 GParespectively. The bulk and shear modulus of the dry rock K_(dry),G_(dry) as estimated using empirical relations according to A. Nur, G.Mavko, J. Dvorkin and D. Galmudi (1998), “Critical Porosity: A Key ToRelating Physical Properties To Porosity In Rocks”, The Leading Edge17(3): 357-362.

$\begin{matrix}{K_{dry} = {K_{s}\left( {1 - \frac{\phi}{\phi_{c}}} \right)}} & {{Equation}\mspace{14mu}(26)} \\{G_{sat} = {G_{dry} = {G_{s}\left( {1 - \frac{\phi}{\phi_{c}}} \right)}}} & {{Equation}\mspace{14mu}(27)}\end{matrix}$

The bulk and shear modulus of the dry rocks set forth in Equations (26)and (27) is determined based on a linear interpolation. For sandstoneaccumulations the critical porosity φ_(c) is 40%.

The combined effect of the rock fluids K_(fluid) is given by VoigtrelationshipK _(fluid) =sK _(water)+(1−S)K _(oil)  Equation (28)

The density of the sandstone rock matrix is ρ_(rock)=2850 Kg/m³, thedensities of oil and water are respectively ρ_(oil)=859 Kg/m³ and anρ_(water)=1014 Kg/m³.

The pressure dependence is not included in these relationships, as it isassumed not to vary significantly over the reservoir life span due tothe voidage replacement recovery process being used to produce thisreservoir. The initial pressure is 30 MPa.

Well Bottomhole pressure (WBHP), well oil production rate (WOPR) andwell water (WWCT) are observed during this study every 30 days for eachwell in the model to mimic realistic conditions. Time-Lapse attributesare derived from reservoir properties. Data (production or time-lapseattributes) is obtained by forwarding the simulator in time. At the endof each model time step production data and/or seismic data can beprovided. However, seismic data is generated only twice during theentire simulation, before the production starts and after a certainperiod of time, such as approximately mid-life of the production fromthe reservoir study model.

In actual practice, the true model is not known. It must therefore beestimated. Using a Monte Carlo approach 80 models were created toinvestigate the impact of uncertainties in the porosity and permeabilityfields in the simulations. Porosity distributions were generated usingSequential Gaussian Simulation while permeability was obtained usingco-kriging. A limited number of points from the true distribution wereused in the kriging setup to populate the porosity (these data pointsrepresent the log data collected at each well). To generate permeabilitythe porosity was used as a secondary attribute in the co-krigingprocess.

The impact of the uncertainties in the porosity and permeability mapsare responsible for huge uncertainties in the total amount of oil thatcan be recovered in the field as seen in FIG. 12. FIG. 13 is a plot offorecast oil production for the models. The ensemble members areindividually represented in gray. The true values are represented inred. The ensemble average is represented in blue. The P90 probabilitycurve in magenta and the P10 in green. The uncertainty in the cumulativeproductions is about 11 millions of barrels of oil, which at currentmarket prices exceeds 1 billion of dollars (FIG. 12). There is a hugeuncertainty in the oil peak as well (FIG. 13). The true model peaksafter 12 years of production while the uncertainty in the initialensemble ranges from 9 to 14 years.

History Matching Production Data

The objective of this experiment is to provide a baseline forcomparison. Most of the oil and gas industry still only uses productiondata to perform history matching, therefore a significant improvement inthe history matching quality can be obtained by the inclusion ofadditional datasets in the history matching process.

The initial ensemble created previously was updated sequentially usingthe EnKF (FIG. 4). In this experiment, 8 years of production data werehistory matched. The simulations are forwarded in time and productiondata is assimilated at the end of each assimilation time step. Theobtained results are shown in FIGS. 14 and 15, where the firstrepresents the field cumulative production and the second figurerepresents the field oil production rate. The ensemble mean is shown inFIGS. 14 and 15 in blue while the ensemble members are shown in grey.The true solution is shown in red. The ensemble average underestimatethe cumulative production (forecast values).

The most important parameter affecting the reservoir performance in thisparticular scenario is thus the porosity distribution. Porositydistribution determines the initial amount of oil initially in place andits location; thus, it affects the total amount of fluids that can berecovered from this field. Permeability plays a major role to explainhow the fluids move inside the field and how fast they can be recovered.But over time, permeability does not significantly affect the cumulativeoil production in this study model due to the high quality sandsimulated in this scenario.

At the end of the history matching experiment the uncertainty in theduration of the production plateau and the cumulative production isstill considerable. A possibility to further improve the quality of thesimulation model is the inclusion of time-lapse data in the historymatching process. A qualitative comparison of the estimated porosity andpermeability can be drawn from the FIGS. 16 and 17 where the estimatedporosity and permeability are shown and FIGS. 7 and 8 where the realproperties are shown.

Joint History Matching Production and Time-Lapse Acoustic Impedance

The state of art technique used in the industry is the utilization ofproduction and time-lapse seismic data in the history matching process.The seismic data is acquired at surface by deploying sources andreceivers in the field.

Gassmann's equations (Equation 12 and Equation 14) and Equation 15 wereused to simulate the acoustic impedance at every grid cell for each ofthe realizations taking in account fluid displacement effects on thereservoir due to production. A base survey is performed before theproduction begins and a monitor survey is performed at the end of thehistory matching period. The relative acoustic impedance difference(Equation 25) is then assimilated in the history matching loop alongwith production data.

The workflow used to incorporate the seismic data into the historymatching process is shown in the FIG. 3. The predicted relativedifference in the time-lapse acoustic impedance due to productioneffects can reach up to about 5% along the production life of thereservoir far exceeding the uncertainty related with the time-lapsesignal, assumed to be 2% in our simulations. This predicted time-lapsedifference was then jointly assimilated with production data.

It was found that assimilating production data for a period of 8 yearsis enough to obtain reasonable results, with comparable history matchingimprove to those obtained assimilating production data for 12 years(FIGS. 28 and 29). The estimated porosity and permeability distributionsat the end of the history matching period can be seen in the FIGS. 20and 21. The best scenario found was to perform the second seismic surveyat the end of the observed production period. By doing this thedifference between two consecutive surveys will be maximized.

Joint History Matching Production and Crosswell Time-Lapse Data

The present invention provides for the use of crosswell data to map thefluid changes in the reservoir. This approach has several advantagesover conventional time-lapse seismic acquisitions. The most importantone is the cost to obtain the data. Running a full field survey isseveral times more expensive than collecting data at certain locationsonly. Reproducibility is also a major issue. Reproducing the acquisitionsetup of surface seismic surveys is challenging and can severelycompromise the quality of the time-lapse data. The time-lapse crosswelldata can be used in several forms under the proposed workflow, amongthem in the form of travel time data or in the form of acousticattributes (as velocity and impedance for example).

Fluid displacement data can be directly obtained from the travel time ofthe rays between the producers and the injectors. The travel time datacontains information about the water flood front movement. The same istrue for the acoustic attributes (velocity and impedance).

This approach has several advantages over conventional time-lapseseismic acquisitions. The most important one it the cost to obtain thedata. Running a full field survey is several times more expensive thancollecting data only at certain locations. Reproducibility of earliersurface survey conditions is also a major issue. Reproducing theacquisition setup of the base survey is challenging and can severelycompromise the quality of the time-lapse data obtained. The advantage ofusing wells as fixed points to collect data avoids this problem.

Another advantage of the present invention is the use of highfrequencies to image the interwell region, which leads to higher spatialresolution. Higher frequencies can also highlight the fluid displacementeffect more easily. The uncertainties in the data are much smaller. Theuse of crosswell tomography can provide a velocity map directly whichthen can be modeled using the Biot velocity model. These advantagesoffset the limited area coverage available with crosswell surveying.

To illustrate the potential of this methodology we used velocitytomograms as the time-lapse data. The observed data was perturbed withGaussian errors with zero mean and standard deviation of 2% of thesignal (time-lapse difference) as described previously (Equation 25).The assimilation results are shown in FIGS. 22 and 23 where theuncertainty in the cumulative production and in the duration of theproduction plateau are shown respectively. A significant improvement inthe quality of the estimates is obtained by the joint assimilation ofproduction and crosswell data. The RRMS error of the estimated porosityof the joint assimilation of production and time-lapse crosswell data iscomparable with the one obtained assimilating production and time lapseacoustic impedance (surface seismic) as seen in the FIG. 28.

A qualitative comparison of the estimated porosity and permeability canbe seen in the FIGS. 24 and 25 where the estimated parameters are shownand FIGS. 7 and 8 where the real parameters are shown. A quantitativecomparison can be seen in FIGS. 28 and 29. The improvement achieved byincorporating time-lapse data is noticeable. The major difference takesplace in the last assimilation time step (8 years) where the time-lapsedata is incorporated. The improvements in the quality of the recoveredporosity and permeability as well as predicted reservoir performance putthe use of production and crosswell data somewhere in between theimprovements obtained by the use of production and time-lapse (surfaceseismic) data. It must be noticed that the proposed methodology isintended for areas that re-shooting surface seismic is not an option.Therefore the use of time-lapse data can significantly enhance thequality of the history matching process.

Significant improvements can also be obtained using the seismic datadirectly (recorded seismic waves). This alternative requires minimalpre-processing and can be used to directly incorporate the crosswellseismic data in the history matching workflow. The only requiredmodification of the workflow is the incorporation of a ray-tracingmodule, which will be used in conjunction with the petro-elastic moduleto simulate the seismic response of the medium.

To exemplify this alternative methodology we assimilated zero-offsettravel-time data in an analogous way as the previous workflow. The onlydifference being the type of crosswell data being included in thehistory matching process. The zero-offset travel-time data is the timerequired to the waves to travel from the sources to the receivers. Thiszero-offset travel time was calculated based on a ray-tracing package.

The results obtained in scenario are shown in the FIGS. 26 and 27 Theimprovements in the history matching are not as significant as beforebut still considerable when compared with the baseline. The time-lapsedata obtained under these circumstances is indicative of the water floodfront movement, as the water saturation increases from the injectortowards the producer. Thus for real applications it may not allow fineresolution updates, however a critical information, the water flooddisplacement can still be captured.

In certain scenarios the use of Gassmann equations may becomeinadequate. This is the case when high frequencies (higher than 100 Hz)are used in the seismic survey to image poorly consolidated sandstonesfor example. Gassmann equations do not take into account attenuation dueto viscous flow.

It is important to highlight that the V_(p) component derived from theBiot's model is an upper limit to high frequencies. In real casescenarios, the frequencies used in such imaging technique are in anintermediate range, usually between 400 Hz to 2.5 kHz. For some rocktypes the velocity dispersion effect can be observed even at seismicfrequencies, which is the case for some sandstone sediments as explainedby Masson, Y. J., Pride, R. S., Nihei, K. T., 2006, Finite DifferenceModeling Of Biot's Poroelastic Equations At Seismic Frequencies, JournalOf Geophysical Research: Solid Earth (1978-2012) 111 (B10).

To overcome this limitation, the Petro-Elastic Module M of the presentinvention uses, as noted above, the fast velocity component of the Biotmode, which is obtained from seismic tomography. This avoids the need toinvert the data (seismic inversion to obtain the acoustic impedance).The fast velocity component, which is more sensitive to fluiddisplacement, can used as time-lapse data attribute.

The present invention, can take advantage of Biot equation modelingmethodology is through the use of crosswell data. The source frequenciesused for such surveys can be much higher than the ones used in surfaceseismic surveys for 4D surveying. An additional advantage in this casethe quality and significance of the data provided. At high frequencies,the V_(p) component of the velocity field becomes more sensitive tofluid displacement, providing more information about the fluiddisplacement in the reservoir. This may be challenging to measure inpractical applications due to the range of frequencies used in realstudies; for most rocks the velocity dispersion effect is only observedat laboratory frequencies exceeding several MHz. This approach may stillhowever yield good results in rock formations where the criticalfrequency is low enough to enable velocity dispersion observations atthe range of imaged frequencies.

The assimilation results obtained using the fast velocity component aresummarized in the FIGS. 30 and 31. All the simulations assume astipulated error (STD) of 2%. Crosswell experiments provide highresolution data, the uncertainty expected in such scenario is small. Thefeasibility of using high frequency time-lapse crosswell experiments toimprove history matching results can be observed in FIG. 32. FIG. 32 isa comparison plot of improvement in the porosity estimate according tothe seismic attribute and configuration used. The crosswell approach canbe compared against a full field time-lapse seismic survey where theacoustic impedance is used as seismic attribute. For small uncertaintiesin the dataset the amount of data present (full field time-lapse survey)provides more information, but as the quality of the datasetdeteriorates crosswell experiments become more robust. Consequently, themethodology of the present invention can generate as much information asthe currently used ones for history matching purposes.

The primary problem solved is the issue with acquisition and processingof 4D data in challenging conditions (onshore reservoirs withalterations over time in the surface environment making it impossible toreshoot seismic) that prevents 4D data being available for use inhistory matching studies for onshore reservoirs.

CONCLUSION

The time-lapse crosswell dataset contains information about the fluiddisplacement movement in the medium, making such data ideal for historymatching applications. This dataset is easier to be obtained thanconventional surface seismic and cheaper.

The acquisition setup can easily be reproduced, which is not usuallypossible in surface seismic surveys (onshore). The cost is also reducedconsiderably because the data is collected only at specific locations.In addition, the higher spatial resolution (cross-section) andsensitivity of the data to the fluid content allows the construction ofa more detailed model.

Further, the acquisition of crosswell data is lapsed in time. At thesame location and using the same initial configuration, more than onesurvey is performed, each at different times after fluid movement as aresult of reservoir production. The time-lapse difference between thesurveys it then incorporated in the history matching process. This isefficiently performed by an automated history matching workflow based onEnsemble Kalman Filtering (EnKF). A petrophysical model in thePetro-Elastic Module is built to predict rock properties (velocity andacoustic impedance) based on reservoir properties (pressure, saturation,porosity, permeability and other if desired) as these vary duringproduction from the reservoir. The petrophysical model with the presentinvention replaces the standard Gassmann's equations which do not takein account attenuation and dispersion at higher frequencies.

The EnKF methodology uses a set of geological realizations to take theinitial uncertainty in the model and by a probabilistic inversionprocess (Bayesian inversion). During the EnKF update porosity,permeability, saturation and pressure are corrected to better match theproduction and time lapse data collected. Thus a set is history matchedmodels is produced. Consequently an uncertainty range is also providedfor the forecast model.

The velocity attribute can be mapped through a crosswell tomography andassimilated directly in the history matching workflow. There is no needto perform a seismic inversion to obtain the acoustic impedanceattribute. This reduces the computational cost required to process thedata and incorporate it in the data assimilation workflow.

An unexpected feature obtained from this methodology is the mitigationof a common problem faced during the assimilation of 4D seismic datausing Ensemble Kalman Filtering. The overshooting problem in porosityand permeability estimation. 4D seismic data is spatially dense whileproduction data is sparse. The smaller quantity of production dataavailable for history matching leads to an overshooting problem. Byusing the present methodology the amount of seismic data used is severalorders of magnitude smaller, leading to a more balanced trade-offbetween time lapse and production data.

The invention has been sufficiently described so that a person withaverage knowledge in the matter may reproduce and obtain the resultsmentioned in the invention herein Nonetheless, any skilled person in thefield of technique, subject of the invention herein, may carry outmodifications not described in the request herein, to apply thesemodifications to a determined methodology, or in the performance andutilization thereof, requires the claimed matter in the followingclaims; such structures shall be covered within the scope of theinvention.

It should be noted and understood that there can be improvements andmodifications made of the present invention described in detail abovewithout departing from the spirit or scope of the invention as set forthin the accompanying claims.

What is claimed is:
 1. A method of mapping fluid displacement changes inan onshore reservoir producing hydrocarbon fluids from wells by historymatching in a computer a reservoir model of the reservoir based onactual production from the reservoir over time and on determinedreservoir formation permeability, the computer having a memory, aprocessor, a reservoir simulator module, a petro-elastic module, ahistory matching module and an output display, the method of mappingfluid displacement changes from time lapse differences in crosswellseismic surveys of the reservoir and history matching of predictedreservoir performance comprising the steps of: (a) conducting a baselinecrosswell seismic survey between wells in the reservoir beforeproduction of fluids from the reservoir; (b) conducting a subsequentcrosswell seismic survey between wells in the reservoir duringproduction from the reservoir; (c) storing in the memory computeroperable instructions causing the computer to map the fluid displacementchanges in the reservoir over time by performing the steps of: (d)forecasting production performance rates and pressures from thereservoir with the reservoir simulator module under control of thestored computer operable instructions; (e) processing the baselinecrosswell seismic survey in the processor of the computer under controlof the stored computer operable instructions to provide a baselinereservoir formation permeability by performing the steps of: (1)obtaining in the computer travel times of seismic energy between thewells during the baseline crosswell seismic survey; (2) performingcrosswell tomography in the computer on the obtained travel times toobtain crosswell baseline tomography; (3) determining from the crosswellbaseline tomography a baseline reservoir formation permeability; (f)updating the reservoir simulator module with the baseline reservoirformation permeability under control of the stored computer operableinstructions to determine with the updated reservoir simulation modulepredicted reservoir performance rates and pressures over time duringproduction from the reservoir; (g) determining with the petro-elasticmodule under control of the stored computer operable instructions abaseline crosswell seismic survey between the wells in the reservoir;(h) the reservoir simulator module under control of the stored computeroperable instructions forwarding in time during production from thereservoir; (i) determining with the petro-elastic module under controlof the stored computer operable instructions a monitor crosswell seismicsurvey between the wells in the reservoir after fluid displacement inthe reservoir and lapse of time during production from the reservoir;(j) determining under control of the stored computer operableinstructions a time lapse difference between the monitor crosswellsurvey and the baseline crosswell seismic survey; (k) performing undercontrol of the stored computer operable instructions history matching inthe history matching module of the predicted reservoir performance rateswith the predicted reservoir performance rates and pressures duringfluid production from the reservoir; and (l) adjusting the reservoirmodel with the reservoir simulator module under control of the storedcomputer operable instructions for mapping fluid displacement changes inthe reservoir based on the performed history matching and the determinedtime lapse differences; and (m) forming with the output display undercontrol of the stored computer operable instructions an output image ofthe adjusted reservoir model to map the fluid displacement changes inthe reservoir over time.
 2. The method of claim 1, further including thestep of: performing in the computer under control of the stored computeroperable instructions a forecast of production from the reservoir withthe adjusted reservoir model.
 3. The method of claim 1, furtherincluding the step of: storing in the memory of the computer undercontrol of the stored computer operable instructions the updated valueof the reservoir formation permeability after fluid displacement andlapse of time.
 4. The method of claim 1, further including the step of:the output display forming under control of the stored computer operableinstructions an output image from the computer of the updated value ofthe reservoir formation permeability after fluid displacement.
 5. Themethod of claim 1, wherein the petro-elastic module in performing thestep of determining an updated value of the reservoir formationpermeability performs the step of: forming a Biot velocity model basedon the crosswell tomography.
 6. The method of claim 1, wherein thehistory matching module in performing history matching performs the stepof: performing Ensemble Kalman filtering in the computer of thereservoir formation permeability data to condition the reservoir model.7. A computer implemented method of mapping fluid displacement changesin an onshore reservoir producing hydrocarbon fluids from wells byhistory matching a reservoir model of the reservoir based on actualproduction from the reservoir over time and on at least one determinedreservoir formation permeability, based on results of a baselinecrosswell seismic survey conducted between wells in the reservoir beforeproduction of fluids from the reservoir to provide a baseline crosswellseismic survey and further based on a subsequent crosswell seismicsurvey between the wells in the reservoir during production from thereservoir for history matching, the method being performed in a dataprocessing system having a memory, a processor, a reservoir simulatormodule, a petro-elastic module, a history matching module and an outputdisplay, the method of mapping fluid displacement changes- comprisingthe computer implemented steps of: (a) storing in the memory computeroperable instructions causing the data processing system to map thefluid displacement changes in the reservoir over time by performing thesteps of:. (b) forecasting production performance rates and pressuresfrom the reservoir with the reservoir simulator under control of thestored computer operable instructions; (c) processing the baselinecrosswell seismic survey in the processor under control of the storedcomputer operable instructions to provide a baseline formationpermeability for the history matching by performing the steps of: (1)obtaining in the computer travel times of seismic energy between thewells during the baseline crosswell seismic survey; (2) performingcrosswell tomography in the computer on the obtained travel times toobtain crosswell baseline tomography; (3) determining from the crosswellbaseline tomography a baseline reservoir formation permeability; (d)updating the reservoir simulator module with the baseline reservoirformation permeability under control of the stored computer operableinstructions to determine with the updated reservoir simulation modulepredicted reservoir performance rates and pressures over time duringproduction from the reservoir; (e) determining with the petro-elasticmodule under control of the stored computer operable instructions abaseline crosswell seismic survey between the wells in the reservoir;(f) the reservoir simulator module under control of the stored computeroperable instructions forwarding in time during production from thereservoir; (g) determining with the petro-elastic module under controlof the stored computer operable instructions a monitor crosswell seismicsurvey between the wells in the reservoir after fluid displacement inthe reservoir and lapse of time during production from the reservoir;(h) performing under control of the stored computer operableinstructions history matching in the history matching module of thecomputer of the forecast reservoir performance rates and pressures withthe updated reservoir performance rates and pressures during fluidproduction from the reservoir; (i) adjusting the reservoir model withthe reservoir simulator module under control of the stored computeroperable instructions for mapping fluid displacement changes in thereservoir based on the performed history matching and the determinedtime lapse differences; and (j) forming with the output display undercontrol of the stored computer operable instructions an output image ofthe adjusted reservoir model to map the fluid displacement changes inthe reservoir over time.
 8. The computer implemented method of claim 7,further including the computer implemented step of: performing in theprocessor under control of the stored computer operable instructions aforecast of production from the reservoir with the adjusted reservoirmodel.
 9. The computer implemented method of claim 7, further includingthe computer implemented step of: storing in the memory of the computerunder control of the stored computer operable instructions the updatedvalue of the reservoir formation permeability after fluid displacement.10. The computer implemented method of claim 7, further including thecomputer implemented step of: forming with the output display undercontrol of the stored computer operable instructions an output image ofthe updated value of the reservoir formation permeability after fluiddisplacement.
 11. The computer implemented method of claim 7, whereinthe petro-elastic module in performing the step of determining anupdated value of the reservoir formation permeability performs the stepof: forming a Biot velocity model based on the crosswell monitortomography.
 12. The computer implemented method of claim 7, wherein thehistory matching module in performing history matching performs the stepof: performing Ensemble Kalman filtering of the reservoir formationpermeability data to condition the reservoir model.
 13. A dataprocessing system for mapping fluid displacement changes in an onshorereservoir producing hydrocarbon fluids from wells by history matching areservoir model of the reservoir based on actual production from thereservoir over time and based on at least one determined reservoirformation permeability from a baseline crosswell seismic surveyconducted between wells in the reservoir before production of fluidsfrom the reservoir and further based on a subsequent crosswell seismicsurvey between the wells in the reservoir during production from thereservoir for the history matching, the data processing systemcomprising: (a) a memory storing computer operable instructions causingthe data processing system to map the fluid displacement changes in thereservoir over time; (b) a processor under control of the storedcomputer operable instructions providing a baseline formationpermeability for the history matching by performing the steps of: (1)obtaining in the computer travel times of seismic energy between thewells during the baseline seismic survey; (2) performing crosswelltomography in the computer on the obtained travel times to obtaincrosswell baseline tomography; (3) determining from the crosswellbaseline tomography a baseline reservoir formation permeability; (c) areservoir simulator module determining forecast reservoir performancerates and pressures over time; (d) a petro-elastic module under controlof the stored computer operable instructions determining a baselinecrosswell seismic survey between the wells in the reservoir; (e) thereservoir simulator under control of the stored computer operableinstructions forwarding in time during production from the reservoir;(f) the petro-elastic module further operating under control of thestored computer operable instructions to determine a monitor crosswellseismic survey between the wells in the reservoir after fluiddisplacement in the reservoir and lapse of time during production fromthe reservoir; (g) the processor further determining under control ofthe stored computer operable instructions a time lapse differencebetween the monitor crosswell survey and the baseline crosswell seismicsurvey; (h) history matching module under control of the stored computeroperable instructions performing history matching of the predictedreservoir performance rates and pressures after fluid production fromthe reservoir; (i) the reservoir simulator module under control of thestored computer operable instructions adjusting the reservoir model formapping fluid displacement changes in the reservoir based on theperformed history matching and the determined time lapse differences;and (j) an output display under control of the stored computer operableinstructions to form a display of the adjusted reservoir model to mapthe fluid displacement changes in the reservoir over time.
 14. The dataprocessing system of claim 13, further including the processor undercontrol of the stored computer operable instructions to perform the stepof: performing a forecast of production from the reservoir with theadjusted reservoir model.
 15. The data processing system of claim 13,wherein the petro-elastic module in determining an updated measure ofthe reservoir formation permeability performs the step of: forming aBiot velocity model based on the crosswell monitor tomography.
 16. Thedata processing system of claim 13, wherein the history matching modulein performing history matching performs step of: performing EnsembleKalman filtering of the reservoir formation permeability data tocondition the reservoir model.
 17. A method of mapping fluiddisplacement changes in an onshore reservoir producing hydrocarbonfluids from wells by history matching in a computer a reservoir model ofthe reservoir based on actual production from the reservoir over timeand on at least one determined reservoir formation porosity, thecomputer having a memory, a processor, a reservoir simulator module, apetro-elastic module, a history matching module and an output display,the method of mapping fluid displacement changes from time lapsedifferences in crosswell seismic surveys of the reservoir and historymatching of predicted reservoir performance comprising the steps of: (a)conducting a baseline crosswell seismic survey between wells in thereservoir before production of fluids from the reservoir to provide abaseline seismic survey for history matching; (b) conducting asubsequent crosswell seismic survey between wells in the reservoirduring production from the reservoir; (c) storing in the memory computeroperable instructions causing the computer to map the fluid displacementchanges in the reservoir over time by performing the steps of: (d)forecasting production performance rates and pressures from thereservoir with the reservoir simulator module under control of thestored computer operable instructions; (e) processing the baselinecrosswell seismic survey in the processor of the computer under controlof the stored computer operable instructions to provide a baselinereservoir formation porosity by performing the steps of: (1) obtainingin the computer travel times of seismic energy between the wells duringthe baseline crosswell seismic survey; (2) performing crosswelltomography in the computer on the obtained travel times to obtaincrosswell baseline tomography; (3) determining from the crosswellbaseline tomography a baseline reservoir formation porosity; (f)updating the reservoir simulator module with the baseline reservoirformation porosity under control of the stored computer operableinstructions to determine with the updated reservoir simulation modulepredicted reservoir performance rates and pressures rates and pressuresover time during production from the reservoir; (g) determining with thepetro-elastic module under control of the stored computer operableinstructions a monitor crosswell seismic survey between the wells in thereservoir after fluid displacement in the reservoir and lapse of timeduring production from the reservoir; (h) determining under control ofthe stored computer operable instructions a time lapse differencebetween the monitor crosswell survey and the baseline crosswell seismicsurvey; (i) performing under control of the stored computer operableinstructions history matching in the history matching module of thepredicted reservoir performance rates with the predicted performancerates and pressures during fluid production from the reservoir; (j)adjusting the reservoir model with the reservoir simulator module undercontrol of the stored computer operable instructions for mapping fluiddisplacement changes in the reservoir based on the performed historymatching and the determined time lapse differences; and (k) forming withthe output display under control of the stored computer operableinstructions an output image of the adjusted reservoir model to map thefluid displacement changes in the reservoir over time.
 18. A computerimplemented method of mapping fluid displacement changes in an onshorereservoir producing hydrocarbon fluids from wells by history matching areservoir model of the reservoir based on actual production from thereservoir over time and on at least one determined reservoir formationporosity, based on results of a baseline crosswell seismic surveyconducted between wells in the reservoir before production of fluidsfrom the reservoir to provide a baseline crosswell seismic survey andfurther based on a subsequent crosswell seismic survey between the wellsin the reservoir during production from the reservoir for historymatching, the computer having a memory, a processor, a reservoirsimulator module, a petro-elastic module, a history matching module andan output display, the method of mapping fluid displacement changescomprising the computer implemented steps of: (a) storing in the memorycomputer operable instructions causing the computer to map the fluiddisplacement changes in the reservoir over time by performing the stepsof:. (b) forecasting production performance rates and pressures from thereservoir with the reservoir simulator module under control of thestored computer operable instructions; (c) processing the baselinecrosswell seismic survey in the processor under control of the storedcomputer operable instructions to provide a baseline formation porosityfor the history matching by performing the steps of: (1) obtaining inthe computer travel times of seismic energy between the wells during thebaseline crosswell seismic survey; (2) performing crosswell tomographyin the computer on the obtained travel times to obtain crosswellbaseline tomography; (3) determining from the crosswell baselinetomography a baseline reservoir formation porosity; (d) updating thereservoir simulator module with the baseline reservoir formationpermeability under control of the stored computer operable instructionsto determine with the updated reservoir simulation module predictedreservoir performance rates and pressures over time during productionfrom the reservoir; (e) determining with the petro-elastic module undercontrol of the stored computer operable instructions a baselinecrosswell seismic survey between the wells in the reservoir;(f)forwarding the reservoir simulator under control of the storedcomputer operable instructions in time during production from thereservoir; (g) determining with the petro-elastic module under controlof the stored computer operable instructions a monitor crosswell seismicsurvey between the wells in the reservoir after fluid displacement inthe reservoir and lapse of time during production from the reservoir;(h) performing under control of the stored computer operableinstructions history matching in the history matching module of thecomputer of the predicted reservoir performance rates and pressuresafter fluid production from the reservoir and passage of time; (i)adjusting the reservoir model with the reservoir simulator module undercontrol of the stored computer operable instructions for mapping fluiddisplacement changes in the reservoir based on the performed historymatching and the determined time lapse differences; and (j) forming withthe output display under control of the stored computer operableinstructions an output image of the adjusted reservoir model to map thefluid displacement changes in the reservoir over time.
 19. A dataprocessing system for mapping fluid displacement changes in an onshorereservoir producing hydrocarbon fluids from wells by history matching areservoir model of the reservoir based on actual production from thereservoir over time and based on at least one determined reservoirformation porosity from a baseline crosswell seismic survey conductedbetween wells in the reservoir before production of fluids from thereservoir and further based on a subsequent crosswell seismic surveybetween the wells in the reservoir during production from the reservoirfor the history matching, the data processing system comprising: (a) amemory storing computer operable instructions causing the dataprocessing system to map the fluid displacement changes in the reservoirover time; (b) a processor operating under control of the storedcomputer operable instructions to provide a baseline formation porosityfor the history matching by performing the steps of: (1) obtaining inthe computer travel times of seismic energy between the wells during thebaseline seismic survey; (2) performing crosswell tomography in thecomputer on the obtained travel times to obtain crosswell baselinetomography; (3) determining from the crosswell baseline tomography abaseline reservoir formation porosity; (c) a reservoir simulator moduledetermining predicted reservoir performance rates and pressures overtime; (d) a petro-elastic module under control of the stored computeroperable instructions determining a baseline crosswell seismic surveybetween the wells in the reservoir; (e) the reservoir simulator moduleunder control of the stored computer operable instructions forwarding intime during production from the reservoir; (f) the petro-elastic modulefurther operating under control of the stored computer operableinstructions to determine a monitor crosswell seismic survey between thewells in the reservoir after fluid displacement in the reservoir andlapse of time during production from the reservoir; (g) the processorfurther determining under control of the stored computer operableinstructions a time lapse difference between the monitor crosswellseismic survey and the baseline crosswell seismic survey; (h) a historymatching module under control of the stored computer operableinstructions performing history matching of the predicted reservoirperformance rates and pressures after fluid production from thereservoir; (i) the reservoir simulator module under control of thestored computer operable instructions adjusting the reservoir model formapping fluid displacement changes in the reservoir based on theperformed history matching and the determined time lapse differences;and (j) an output display operating under control of the stored computeroperable instructions to form a display of the adjusted reservoir modelto map the fluid displacement changes in the reservoir over time.